**
Below is the ascii version of the abstract for 99-278.
The html version should be ready soon.**Simon B.
A Feynman-Kac Formula for Unbounded Semigroups
(12K, LaTeX)
ABSTRACT. We prove a Feynman-Kac formula for Schr\"odinger
operators with potentials $V(x)$ that obey (for
all $\varepsilon >0$)
\[
V(x) \geq -\varepsilon |x|^2 - C_\varepsilon.
\]
Even though $e^{-tH}$ is an unbounded operator, any
$\varphi, \psi \in L^2$ with compact support lie in
$D(e^{-tH})$ and $\langle \varphi, e^{-tH}\psi\rangle$
is given by a Feynman-Kac formula.